A 2 min read

OG 2020: Question No. 96

If rectangle ABCD is inscribed in the circle above, what is the area of the circular region?

1. 36.00π
2. 42.25π
3. 64.00π
4. 84.50π
5. 169.00π

Source	OG 2020
Type	Problem Solving
Topic	Geometry
Sub-Topic	Circle/Triangle
Difficulty	Medium

Solution

Given

In this question, we are given

• Rectangle ABCD is inscribed in the circle, as shown in the given diagram.

To Find

We need to determine

• The area of the circular region

Approach & Working

As ABCD is a rectangle, we can say angle ADC = angle ABC = 90°

• Hence, we can conclude that AC is a diameter of the circle.

(Note that by applying the same logic, we can say angle DAB = angle DCB = 90°, hence, DB is a diameter of the rectangle).

Now, if we connect AC, then applying Pythagoras Theorem we can say

• AC² = AB² + BC²

Or, AC² = 12² + 5² = 144 + 25 = 169 = 13²

Or, AC = 13

Hence, the diameter of the circle is 13 units.

• Radius (r) of the circle = 13 * ½ = 13/2 units
• So, the area of the circle = πr² = π(13/2)² = 169π/4 = 42.25π

Hence, the correct answer is option B.

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